Question:
If \(-13<a<-2\) and \(1<b<9\), which of the following could be equal to the product of \(a\) and \(b\)? Indicate all possible values.
If \(-13<a<-2\) and \(1<b<9\), which of the following could be equal to the product of \(a\) and \(b\)? Indicate all possible values.
Show Hint
For product range questions, calculate extreme values and then verify each option within that interval carefully.
Updated On: Sep 30, 2025
- -20
- -18
- -15
- -14
- -13
- -9
Show Solution
Verified By Collegedunia
The Correct Option is A
Solution and Explanation
Step 1: Define ranges.
Since \( -13<a<-2 \), possible integer values for \( a \) are: \(-12, -11, -10, -9, -8, -7, -6, -5, -4, -3\). Since \( 1<b<9 \), possible integer values for \( b \) are: \(2, 3, 4, 5, 6, 7, 8\).
Step 2: Product range.
Smallest product = \(-12 \times 8 = -96\).
Largest product = \(-3 \times 2 = -6\).
So possible values of \( ab \) are between -96 and -6.
Step 3: Check options.
- -20: Falls in range, possible.
- -18: Falls in range, possible.
- -15: Falls in range, possible.
- -14: Falls in range, possible.
- -13: Not possible (not divisible by given integers).
- -9: Not possible (since \(a\) is negative and \(b\) is positive, but no integer pair matches). Thus, correct answers are -20, -18, -15, -14.
Since \( -13<a<-2 \), possible integer values for \( a \) are: \(-12, -11, -10, -9, -8, -7, -6, -5, -4, -3\). Since \( 1<b<9 \), possible integer values for \( b \) are: \(2, 3, 4, 5, 6, 7, 8\).
Step 2: Product range.
Smallest product = \(-12 \times 8 = -96\).
Largest product = \(-3 \times 2 = -6\).
So possible values of \( ab \) are between -96 and -6.
Step 3: Check options.
- -20: Falls in range, possible.
- -18: Falls in range, possible.
- -15: Falls in range, possible.
- -14: Falls in range, possible.
- -13: Not possible (not divisible by given integers).
- -9: Not possible (since \(a\) is negative and \(b\) is positive, but no integer pair matches). Thus, correct answers are -20, -18, -15, -14.
Was this answer helpful?
0
0
Top GRE Quantitative Aptitude Questions
One pen costs \(\$\)0.25 and one marker costs \(\$\)0.35. At those prices, what is the total cost of 18 pens and 100 markers?
- Working alone at its constant rate, machine A produces kkk liters of a chemical in 10 minutes. Working alone at its constant rate, machine B produces kkk liters of the chemical in 15 minutes. How many minutes does it take machines A and B, working simultaneously at their respective constant rates, to produce kkk liters of the chemical?
- If the dollar amount of sales at Store P was $800,000 for 2006, what was the dollar amount of sales at that store for 2008?
- At Store T, the dollar amount of sales for 2007 was what percent of the dollar amount of sales for 2008? Give your answer to the nearest 0.1%.
- If the ratio of A to B is 3:4 and the ratio of B to C is 5:6, what is the ratio of A to C?
View More Questions
Top GRE Number System Questions
- How many integers from 3 to 30, inclusive, are odd?
- The greatest prime factor of 144 is \( x \)
The greatest prime factor of 96 is \( y \) - Dharik lives in a house on a straight street. For years, there have been 16 houses on his street to the right of his house and 17 houses on his street to the left of his house. Last year, 5 new houses were built on the same street even further to the left of those houses to the left of Dharik’s house. If these are the only houses on this street, how many houses are on this street?
- Let \( p = 4 \times 6 \times 11 \times n \), where \( n \) is a positive integer. Compare the following:
Quantity A: Remainder when \( p \) is divided by 5
Quantity B: Remainder when \( p \) is divided by 33 - How many five-digit numbers can be formed using the digits 0, 2, 3, 4 and 5, when repetition is allowed, such that the number formed is divisible by 2 or 5 or both?
View More Questions
Top GRE Questions
One pen costs \(\$\)0.25 and one marker costs \(\$\)0.35. At those prices, what is the total cost of 18 pens and 100 markers?
- Working alone at its constant rate, machine A produces kkk liters of a chemical in 10 minutes. Working alone at its constant rate, machine B produces kkk liters of the chemical in 15 minutes. How many minutes does it take machines A and B, working simultaneously at their respective constant rates, to produce kkk liters of the chemical?
- If the dollar amount of sales at Store P was $800,000 for 2006, what was the dollar amount of sales at that store for 2008?
- At Store T, the dollar amount of sales for 2007 was what percent of the dollar amount of sales for 2008? Give your answer to the nearest 0.1%.
- If the ratio of A to B is 3:4 and the ratio of B to C is 5:6, what is the ratio of A to C?
View More Questions